Correlating physico-mechanical properties of intact...

Correlating physico-mechanical properties of intactrocks with P-wave velocity

C. Kurtulus1 • F. Sertcelik1 • I. Sertcelik1

Received: 13 April 2015 / Accepted: 9 October 2015� Akademiai Kiado 2015

Abstract The physico-mechanical properties of five different intact rock types including

sandstone, arkoses and limestone were determined through standardized laboratory tests.

Ninety six specimens were tested to obtain the relationships between P-wave velocity (Vp),

dry unit weight (DUW), uniaxial compressive strength (UCS), point load index Is(50),

Brazilian tensile strength (TS), porosity (U), and Schmidt hardness (RN). This study also

reviews some recent correlations between P-wave velocity and physico-mechanical

properties as well as investigates the reliability of these correlations. Findings show the

results of the experimental tests are in good agreement with previous studies. Statistical

equations have been determined for estimating the physico-mechanical properties of rocks

using nondestructive and indirect test methods. Results of regression analysis showed

satisfactory correlations. Based on the results, new strong correlation with correlation

coeffecients above (R2[ 0.80) are introduced for predicting the UCS, Is(50), U and RN

and reasonable good correlations (R2 C 0.78) are introduced to predict TS and DUW from

P-wave velocity of different intact rock core samples. There is a discrepancy between

P-wave velocity (Vp) in situ values with laboratory results. The large reductions in Vp

in situ values are clearly the functions of fractures and natural joints.

Keywords Physico-mechanical properties � Kocaeli (Turkey) � P-wave velocity �Dry unit weight � Porosity

& F. [email protected]

C. [email protected]

I. [email protected]

1 Department of Geophysics, Kocaeli University, Kocaeli, Turkey

123

Acta Geod GeophysDOI 10.1007/s40328-015-0145-1

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1 Introduction

Construction of projects such as foundation on rocks, underground structures, infras-

tructure works, tunnels, dams etc. is substantially influenced by physical and mechanical

properties of rocks. The reason of the most of the hazards is the inaccurate evaluation

of these rock properties. Especially specimen preparation for laboratory testing to

determine the mechanical properties are expensive, difficult to be carried out and time

consuming. In addition, the accuracy is mostly dependent on the specimen dimension,

human errors, instrument calibration and internal factors. For these difficulties, indirect

methods are often applied for preliminary studies. Indirect methods are simple do not

require specimen preparation. The physico-mechanical properties of rocks are deter-

mined according to both the American Society for Testing and Materials ASTM

(1986a) and International Society for Rock Mechanics ISRM (1987) and other common

standards.

The P-wave velocity which depends on density and elastic properties of rocks has

been used for many years to determine the physico-mechanical properties of different

rocks by various authors. Many authors have studied the relations between physico-

mechanical properties and P-wave velocity of rocks. Smorodinov et al. (1970) estab-

lished empirical relation between uniaxial compressive strength (UCS) and den-

sity/porosity. Inoue and Ohomi (1981) determined the relations between UCS and

P-wave velocity of soft rocks. Gaviglio (1989) investigated the relation between P-wave

velocity and density. Boadu (2000) found the transport properties of fractured rocks

from seismic waves. Kahraman (2001a) made correlations between P-wave velocity and

number of joints and Schmidt rebound number (RN). Kahraman (2001b) evaluated the

correlations between UCS, point load index (Is(50)), RN, P-wave velocity and impact

strength index. Kahraman (2002) estimated the P-wave velocity of intact rock from

indirect laboratory measurements. Ozkahraman et al. (2004) obtained the thermal

conductivity of rocks from P-wave velocity. Yasar and Erdogan (2004) correlated

P-wave velocity with density, Young’s modulus and UCS of carbonate rocks. Sharma

and Singh (2008) studied on the correlations between the P-wave velocity, impact

strength index, slake durability index and UCS. Khandelwal and Singh (2009) corre-

lated the P-wave velocity with different physico-mechanical properties of coal measure

rocks. Khandelwal and Ranjith (2010) made correlations of P-wave velocity with index

properties of different rock types. Kurtulus et al. (2010) evaluated the physical and

mechanical properties of Gokceada: Imbroz (NE AegeanSea) Island andesites. Kurtulus

et al. (2011a) studied the physical and mechanical properties of serpentinized ultra basic

rocks in NW Turkey. Kurtulus et al. (2011b) studied the seismic anisotropy of Devo-

nian limestone. Empirical relationships proposed in literature between P-wave velocity

and uniaxial compressive strength (UCS), point load index Is(50), porosity (U),

Brazilian tensile strength (TS) and Schmidt rebound number (RN) are shown in

Table 1. The differences determined could be related to the mineralogical composition

and texture of the rock materials or the different methods used for sampling and

performing the tests.

This paper aims to evaluate the physico-mechanical properties of intact rocks and the

correlation of P-wave velocity with the dry unit weight, uniaxial compressive strength

(UCS), Point Load Index (Is(50)), Brazilian Tensile Strength (TS), porosity (U) and

Schmidt Rebound Number (RN), with the intention of providing detailed documentation

about intact rocks.

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123

2 Research methodology

2.1 Sample collection

The rock samples were collected from five areas in Kocaeli area (Fig. 1).

Laboratory tests were performed on 96 rock specimens, including 10 of which are

volcanic and 86 of them are sedimentary rocks (Table 2).

Table 1 Equations correlating the UCS, Is(50), U, and RN to P-wave velocity for several areas in the worldand references

Equations References

UCS = 56.71 Vp - 192.93 Cobanglu and Celik (2008)

UCS = 0.11Vp - 515.56

UCS = 0.78e0.88Vp Entwisle et al. (2005)

UCS = 0.78Vp0.88

UCS = 9.95Vp1.21 Kahraman (2001b)

UCS = 0.133Vp - 227.19 Khandelwal and Singh (2009)

q = 0.0002(UPV) ? 1.8745 Kurtulus et al. (2010)

Is(50) = 0.0018(UPV) - 1.9906

UCS = 0.1581(UPV)-643.2

RN = 0.0319(UPV) - 92.442

n = -6.10-0.5(UPV) ? 0.0366

UCS = 0.0675(UPV) - 245.13 Across foliation Kurtulus et al. (2011a)

Is(50) = 0.0042(UPV) - 14.602 ‘’

DUW = 0.0002(UPV) ? 1.7752 ‘’

n = -0.0031(UPV) ? 16.736 ‘’

UCS = 0.0188(UPV) - 71.04 Along foliation

Is(50) = 0.0013(UPV) - 4.819 ‘’

DUW = 0.0001(UPV) ? 1.7937 ‘’

n = -0.0029(UPV) ? 16.733 ‘’

Is(50) = 0.0033(UPV) - 7.7876 Across foliation Kurtulus et al. (2011b)

UCS = 0.0533(UPV) - 1326.29 ‘’

n = -0.0011(UPV) ? 5.6858 ‘’

d = 0.0002(UPV) ? 1.6769 ‘’

Is(50) = 0.0016(UPV) - 2.4235 Along foliation

UCS = 0.0207(UPV) - 24.729 ‘’

n = -0.0005(UPV) - 3.3089 ‘’

d = 8E-05(UPV) ? 2.0858 ‘’

UCS = 165.05e(-4.452/vp) Moradian and Behnia (2009)

UCS = 0.0642Vp-117.99 Sharma and Singh (2008)

SV = 4.3183.9q-7.5071 Yasar and Erdogan (2004)

Where (Vp and SV) P-wave velocity, (DUW, d, q) dry unit weight, (UCS) uniaxial compressive strength,Is(50) point load index, (U,n) porosity, (RN, SCH) Schmidt rebound number

Acta Geod Geophys

123

2.2 Laboratory investigation

Core specimens of rock samples collected from five different rock types were cored in NX

size (54 mm diameter) by coring machine. The both ends of the specimens were trimmed

as 110–115 cm (ISRM 1981) and smoothed using a lathe to avoid end effects. The

specimens were dried at 105 �C for 24 h to remove moisture because drying of the

specimens are particularly important not to damage or alter the rock fabric. In addition, dry

weights are absolutely crucial and must be well defined, stable and controlled throughout

handling before, during and after analysis.

2.3 Determination of P-wave velocity

The P-wave velocity of rock specimens was determined using Pundit Plus with the

transducers having a 54.0 KHZ frequency as per the ISRM (ASTM 2001; ISRM 2007).

Figure 2 shows ultrasonic pulse testers used in this study. A mechanical pulses generated

by this instrument are transmitted from one end received at another end of the specimens

by piezo–electric transducers. The velocity is determined by dividing the traveling the

distance (d) to travel time elapsed (t) in traveling the distance by the wave pulse from the

emitter to receiver placed both ends of the specimens, Table 3.

Table 2 List of rock types with class and location

Rock type No of specimen Rock class Lithologic age

Kızderbent volcanic 10 Igneous Lower-middle Eocene

Sopalı Arkose 8 Sedimentary Silurian

Korfez sandstone 36 Sedimentary Lower Ordovician-lower Silurian

Derince sandstone 20 Sedimentary Lower Ordovician-lower Silurian

Akveren limestone 22 Sedimentary Upper Cretaceous-lower Eocene

Fig. 1 Geology map of the research area (TUBITAK 2010). Kızderbent Volcanic, Sopalı Arkose, KorfezSandstone, Derince Sandstone and Akveren Limestone specimens are shown by the star, circle, rectangle,triangle and square, respectively

Acta Geod Geophys

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As seen from Table 3, the velocity of Kızderbent volcanite specimens ranges from

5800.0 to 6340.0 m/s with the mean 6370.0 m/s, whereas that of Sopalı arkose specimens

vary between 2544.0 and 3300.0 m/s with the mean 2922.0 m/s. The velocity of Korfez

sandstone specimens change between 2968.0 and 6010.0 m/s with the mean 4489.0 m/s

and that of Akveren limestone specimens ranges from 4300.0 and 5800.0 m/s with the

mean 5050.0 m/s. The velocity of Derince sandstone specimens vary between 1890.0 and

3300.0 m/s with the mean 2595.0 m/s.

2.4 Determination of different physico-mechanical properties

The effective porosity of rock specimens were determined using saturation method. Dry

unit weights and effective porosity of the rock specimens were determined in accordance

with ISRM (2007). The uniaxial compressive strength (UCS) were obtained by subjecting

each specimen to H incremental loading at about constant rate using a hydraulic testing

machine of 150.0 KN capacity in accordance with ASTM (1986b). The Is (50) of the

specimens was determined by mounting each specimen between two platens of a point load

tester of 50.0 KN capacities in accordance with ASTM (2005). Schmidt hardness of the

specimens was determined according to ASTM D5873 (2014) standard recommendations

on cylindrical specimens using a Schmidt hammer type NR of impact energy of 2.207 Nm.

The Brazilian tensile strength of the specimens of NX diameter were determined using

Brazilian test apparatus equipped with digital display unit for displaying maximum load.

Rock specimens were loaded diametrically between the loading platens of the apparatus as

per ISRM (1978) standards.

2.5 Geophysical survey

The seismic refraction surveys were conducted at Kızderbent volcanites, Sopalı Arkose,

Korfez sandstone, Akveren limestone and Derince sandstone in the investigation area to

correlate the ultrasonic pulse velocities of rock specimens with dynamic P-wave velocities.

The seismic refraction data were recorded using a 12 channel Geometrics Seismic

Enhancement (Smart Seis) seismograph. The first arrival phases assumed to be refracted

from the same interface, the P-wave velocities were calculated from the slope of the line

connecting the first arrival phases using GeoSeis computer program. The determined

average P-velocities are given in Table 4.

The discrepancy increases notably when comparing Vp in situ values with laboratory

results. The large reductions in Vp in situ values are clearly the functions of fractures and

Fig. 2 Ultrasonic pulse testerinstruments

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Table 3 Vp, DUW, UCS, Is(50), TS, U, and RN test results

B DUW(g/cm3)

UCS (MPa) Is(50) (MPa) TS (MPa) U (%) RN Formation

5800 2.68 172.0 13.5 57.0 0.048 51.0 Kızderbent volcanites










3153 2.43 18.0 1.86 29.0 0.278 32.0 Sopalı Arkose

3159 2.38 18.0 1.76 25.0 0.276 32.0 Sopalı Arkose

2544 2.31 11.6 0.93 29.0 0.24 24.0 Sopalı Arkose

3160 2.32 23.5 1.88 35.0 0.249 32.0 Sopalı Arkose

2668 2.25 12.35 1.13 23.0 0.26 29.0 Sopalı Arkose

2918 2.18 15.375 1.23 33.0 0.23 31.0 Sopalı Arkose

3255 2.51 23.5 2.1 38.0 0.25 32.0 Sopalı Arkose

3300 2.46 28.0 2.24 38.0 0.23 32.0 Sopalı Arkose

5150 2.63 102.34 8.19 55.0 0.1 49.0 Korfez sandstone

























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Table 3 continued

B DUW(g/cm3)













5300 2.4 126.0 9.6 55.0 0.08 51.0 Akveren limestone






















2210 1.68 13.86 1.11 27.0 0.29 23.0 Derince sandstone










Acta Geod Geophys

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natural joints. P-wave velocity depends on mineralogical composition, micro cracks and

pores of the rocks and on the physical parameters, such as absorption by weight, density or

porosity.

2.6 Result and discussion

Results of laboratory tests on 96 specimens are listed in Table 3. As can be seen in this

table, volcanic rocks give higher uniaxial compressive strength (UCS) values

(172–202 MPa) and point load index Is(50) compared to sedimentary rocks.

The previous literatures show that our results are in acceptable ranges (Cobanglu and

Celik 2008; Entwisle et al. 2005; Kahraman 2001a; Khandelwal and Singh 2009; Kurtulus

et al. 2010; Kurtulus et al. 2011a; Kurtulus et al. 2011b; Moradian and Behnia 2009;

Sharma and Singh 2008).

In order to describe the relationships between P-wave velocity and physico-mechanical

properties of rocks a regression analysis was carried out. The equation of the best fit line

and the coefficient of determination (R2) were determined for each test result (Figs. 3, 4, 5,

6, 7, 8). It can be seen from the figures that, in all cases, the best fit relationships were

found to be the best.

There is an exponential relation between P-wave velocity and dry unit weight with a

strong correlation of (R2 = 0.795) (Fig. 3). The equation of this relation is given as;

DUW ¼ 0:52V0:45p R2 ¼ 0:795

� �ð1Þ

Table 3 continued

B DUW(g/cm3)












Table 4 Average P-wavevelocities of rocks obtained fromseismic refraction surveys in theinvestigation areas

Investigation area Average P-wave velocity (m/s)

Kızderbent volcanites 4560.0

Sopalı Arkoz 1500.0

Korfez sandstone 1701.0

Akveren limestone 1483.0

Derince sandstone 1493.0

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Polynomial relations have been observed between P-wave velocity and UCS and Is(50)

(Figs. 4, 5). The equations are given below:

UCS ¼ 8:10�6Vp2 � 0:024Vp þ 31:92 R2 ¼ 0:89� �

ð2Þ

Is 50ð Þ¼ 7:10�7V2p � 0:002Vp þ 2:839 R2 ¼ 0:88

� �ð3Þ

A very good correlation (R2 = 0.89) was found between Vp and UCS, and also

(R2 = 0.88) between Vp and Is(50) for P-wave velocity and the tensile strength, effective

porosity and Schmidt rebound number show linear relationships (Figs. 6, 7, 8).

Fig. 3 Graph of dry unit weight (DUW) and P-wave velocity (Vp)

Fig. 4 Graph of uniaxial compressive strength (UCS) and P-wave velocity (Vp)

Fig. 5 Graph of point load index (Is(50)) and P-wave velocity (Vp)

Acta Geod Geophys

123

TS ¼ 0:008Vp þ 3:84 R2 ¼ 0:78� �

ð4Þ

[ ¼ �6E� 05Vp þ 0:383 R2 ¼ 0:85� �

ð5Þ

RN ¼ 0:006Vp þ 9:52 R2 ¼ 0:80� �

ð6Þ

A good correlation (R2 = 0.78) was found between P-wave velocity and Brazilian

tensile strength, (R2 = 0.85) between Vp and Ø, and (R2 = 0.80) between Vp and RN.

Fig. 6 Graph of tensile strength (TS) and P-wave velocity (Vp)

Fig. 7 Graph of effective porosity (U) and P-wave velocity (Vp)

Fig. 8 Graph of Schmidt rebound number (RN) and P-wave velocity (Vp)

Acta Geod Geophys

123

From Fig. 7, it may be seen that when, the P- wave velocity increases the porosity

decreases. However, from Figs. 3, 4, 5, 6, and 8 it can be observed that when the P-

wave velocity increases, dry unit weight, uniaxial compressive strength, point load index,

tensile strength and Schmidt rebound number increase. Kızderbent volcanites have the

highest P-wave velocities range between 5800.0 and 6340.0 m/s with the mean

6370.0 m/s and for physico-mechanical properties wherein dry unit weights (DUW) vary

between 2.68 and 2.95 gr/cm3 with the mean 2.815 gr/cm3, uniaxial compressive

strengths (UCS) range from 172.0 to 202.0 MPa with the mean 187.0 MPa, Point load

index (Is (50)) change between 13.6 and 16.32 MPa with the mean 14.96 MPa, Brazilian

tensile strengths range between 53.0 and 65.0 MPa with the mean 59.0 MPa and Schmidt

rebound numbers vary from 51.0 to 60.0 with the mean 55.5. Kızderbent volcanites have

the lowest effective porosity values (U) vary between 0.032 and 0.048 % with the mean

0.04 %. Sopalı Arkoses have the lowest P-wave velocities ranging from 2544.0 to

3300.0 m/s with the mean 2922.0 m/s. Their (DUW) vary between 2.18 and 2.46 gr/cm3

with the mean 2.32 gr/cm3, (UCS) range between 11.6 and 28 MPa with the mean

19.8 MPa, (Is (50)) change between 0.93 and 2.24 MPa with the mean 1.585 MPa, (TS)

range from 25.0 to 38.0 MPa with the mean 31.5 MPa, (RN) change between 24.0 and

32.0 with the mean 28.0. Sopalı arkoses have the highest effective porosities (U) vary

between 0.23 and 0.278 % with the mean 0.254 %. P-wave velocities and physico-

mechanical properties of Korfez sandstone, Akveren limestone and Derince sandstone

follow the Kızderbent volcanites respectively. In general, the correlation coefficients (R2)

were lower for the DUW and TS than for the UCS, Is (50), U and RN (Figs. 3, 4, 5, 6, 7,

8) in this study.

The relation between DUW and Vp is similar to relationship given by Kurtulus et al.

(2011b), but its correlation coefficient (R2 = 0.795) higher than proposed by Kurtulus

et al. (2011b). The proposed relationship between UCS and Vp is similar to suggested

relationships given by Cobanglu and Celik (2008) and Kurtulus et al. (2010), but corre-

lation coefficient is 0.89 which is relatively higher than their suggested correlation coef-

ficients. However, it is relatively lower than correlation coefficients given by Khandelwal

and Singh (2009), Kurtulus et al. (2011a), Sharma and Singh (2008). Our relationship

between Is (50) and Vp is similar to relationships given by Kurtulus et al. (2010), Kurtulus

et al. (2011a), Kurtulus et al. (2011b), but its correlation coefficient (R2 = 0.88) is lower

than that given by Kurtulus et al. (2010), very close to that of others. Relation between RN

and Vp is similar to relationship proposed by Kurtulus et al. (2010), however, its corre-

lation (R2 = 0.80) is higher than their suggested correlation.

3 Conclusions

In this study, the physico-mechanical properties including P-wave velocity, dry unit

weight, uniaxial compressive strength, point load index, indirect tensile strength,

effective porosity, and Schmidt hardness of the intact rocks were determined in the

laboratory. The test results were interpreted statistically and reasonable good relation-

ships were determined with P-wave velocity (ranging between 1890.0 and 6340.0 m/s)

to the physico-mechanical properties. This result denotes that P-wave velocities could

be used in determination of the physico-mechanical properties of intact rocks.

Acta Geod Geophys

123

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